New matrix splitting iteration method for generalized absolute value equations

In this paper, a relaxed Newton-type matrix splitting (RNMS) iteration method is proposed for solving the generalized absolute value equations, which includes the Picard method, the modified Newton-type (MN) iteration method, the shift splitting modified Newton-type (SSMN) iteration method and the Newton-based matrix splitting (NMS) iteration method. We analyze the sufficient convergence conditions of the RNMS method. Lastly, the efficiency of the RNMS method is analyzed by numerical examples involving symmetric and non-symmetric matrices.